Why did Mahaprabhu only write one poem, and left it to his followers to explain everything else?

Mahāprabhu was always in emotional upheaval. In such a state, no one can explain anything clearly or systematically. His close confidants were comparatively calmer – especially Gadādhara, Advaita, and Śrīnivāsa. Their immediate students were calmer still – especially Rūpa and Sanātana. These people had great literary education and talent, and extremely clear intellects well suited for organization and explanation of concepts. We can say their own Nephew and student, Jīva, was even more philosophically inclined and dextrous. Therefore Jīva fulfilled the task of explaining Mahāprabhu’s philosophy (mostly by writing Sandarbha), while Rūpa explained how Mahāprabhu’s yoga should be practiced (mostly in Bhaktirasāmṛta Sindhu) and Sanātana explained how religious and social practices could be applied in that context (mostly in Haribhakti Vilāsa).

What is a devotee?

Someone devoted to something is a devotee.

A vaisnava?

Whatever is related to Viṣṇu is Vaiṣṇava.

A sadhu?

Someone whose character and behavior is sat (good) is sādhu.

A guru? 

One who is gara (big and heavy) is guru. This word, gara, is related to giri – a word for “mountain” which literally means “encompassing.” One who has studied everything, who carries a ton (of books / knowledge), is “guru.” Therefore the word denotes teachers.

Advayataraka Upanishad (Verse 16) offers another angle on the word:

गुशब्दस्त्वन्धकारः स्यात्‌ रुशब्दस्तन्निरोधकः।
अन्धकारनिरोधित्वात्‌ गुरुरित्यभिधीयते॥ १६॥

gu-śabdas tv andhakāraḥ syāt, ru-śabdas tan nirodhakaḥ.
andhakāra nirodhitvāt gurur ity abhidhīyate.

The word “gu” can mean darkness. The word “ru”, its destroyer.
So, the word “guru” has the sense of someone who destroys darkness.

“Darkness” is a metaphor for non-knowing. So, again, the word denotes teachers.

A diksa guru?

One who starts your education. (dīk means “orientation”)

A siksa guru? 

One who actually teaches. (śi means “instruction”).

Now, the above terms but prefixed by the word “genuine” or “pure”? 

A genuine/pure X is always X and nothing but X.